Greatest Common Factor of 63 and 84 by Prime Factorization

Given Numbers: 63, 84
Identify the Prime Factors of 63 and 84 by Prime Factorization

• Prime Factorization of 63: 63 = 3 x 3 x 7 = 3² x 7¹
• Prime Factorization of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3¹ x 7¹

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

• 3 and 7 are Prime Factors common to the Prime Factorizations of 63 and 84

Determine the least number of occurrences of 3 and 7 among the Prime Factorizations:

• 3 occurs at least 1 time in each Prime Factorization
• 7 occurs 1 time in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 63 and 84 is equal to 3 x 7, which equals the product of 3 and 7 raised to the powers of their least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(63, 84) = 3¹ x 7¹
• GCF(63, 84) = 3 x 7
• GCF(63, 84) = 21

Therefore, the Greatest Common Factor of 63 and 84 by Prime Factorization = 21